Identifying Algebraic Properties
Date: 12/29/96 at 19:43:19 From: Kenneth L McConnell Subject: Pre-Algebra Help Dr. Math, My daughter is in a pre-algebra class in the eighth grade. I am trying to understand the following problem so I can help her with a homework assignment. Any information you could give me regarding the following would be greatly appreciated: Choose which property is used to get each step of the solution: a) Additive Identity of Zero b) Associative Property of Addition c) Communitive Property of Addition d) Op-Op property e) Property of Opposites (-3 + 8) + -(-3) =(-3 + 8) + 3 Answer__ Why? = -3 + (8 + 3) Answer__ Why? = -3 + (3 + 8) Answer__ Why? = (-3 + 3) + 8 Answer__ Why? = 0 + 8 Answer__ Why? = 8 Answer__ Why? My primary request is for a definition of "a" through "e" and how they apply to the above. Thank you, Ken McConnell
Date: 12/30/96 at 10:23:03 From: Doctor Rob Subject: Re: Pre-Algebra Help Glad that you are helping your daughter. Perhaps you will both learn something in the process! Your daughter's textbook should be the source for the definitions of the properties you list. The first three properties are standard, while the last two are not, so I can only guess about the meanings of the last two. a) Additive Identity of Zero (STANDARD) Given any number, if you add zero to it, you get that number back. In equations, for any number a, a + 0 = 0 + a = a. b) Associative Property of Addition (STANDARD) Given any three numbers to be added, the result of adding the sum of the first and second to the third is the same as adding the first to the sum of the second and third. In equations, for any three numbers a, b, and c, (a + b) + c = a + (b + c). c) Commutative Property of Addition (STANDARD) Given any two numbers, the result of adding the first to the second is the same as the result of adding the second to the first. In equations, for any two numbers a and b, a + b = b + a. d) Op-Op property (NON-STANDARD) Given any number, the opposite of its opposite is the number itself. In equations, for any number a, -(-a) = a. e) Property of Opposites (NON-STANDARD) Given any number, the sum of it and its opposite is zero. In equations, for any number a, a + (-a) = 0. Now, given this, I think you can figure out which reason goes with which operation. Just match the patterns in the properties with the patterns in the expressions, and see which ones fit. By the way, underlying all of the above reasoning is the following principle: when two numbers are equal, any expression involving the first will remain the same when the second is substituted for it. For example, in the first expression, you find -(-3), and from d) you know that -(-3) = 3, so by this substitution principle, you can replace -(-3) by 3 without changing the value of the expression. If we can help you more, please let us know. -Doctor Rob, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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